Question

what is the sum of a 7-term geometric series if the first term is −6, the last term is −24,576, and the common ratio is −4? −32,766 −19,662 19,662 32,766

Answer 1

Sum of ggeo metric sequence is

Sn=$\frac{a1(1-r^n)}{1-r}$

n=which term
a1=first term
r=common ratio


so
n=7
a1=-6
r=-4

Sn=$\frac{-6(1-(-4)^7)}{1-(-4)}$
Sn=$\frac{-6(1-(-16384))}{1+4}$
Sn=$\frac{-6(1+16384)}{5}$
Sn=$\frac{-6(16385)}{5}$
Sn=$\frac{-98310}{5}$
Sn=-19662

answer is 2nd option os -19662